GE391 Introduction to Geophysics

Homework

Due 10/8/2009

Prof. Alan L. Kafka

Prof. John E. Ebel

1)  For a satellite of small mass orbiting at radius r a much more massive object of mass M, the period of the orbit T can be found from the formula

where T has units seconds.  Estimate the mass of the sun assuming the EarthÕs orbit to be circular with a radius of 1.5 x 108 km.

2) Use a calculation to show that the source of the Mississippi River is about 5 km closer to the center of the Earth than is the mouth of this major river.  Even though this is true, please explain why it does not mean that the water in the river is flowing uphill.

3)  It is observed that the acceleration of gravity g is greater down a mine than at the EarthÕs surface.  Show that this result can be explained if the EarthÕs density increases sufficiently rapidly with depth.

4)  A 500-m deep depression on the EarthÕs surface fills with (a) sandstone of density 2.2 x 103 kg m-3 and (b) ironstone of density 3.4 x 103 kg m-3.  Assuming that isostatic equilibrium is attained, calculate the thickness of sediment that will be deposited.  (Use crustal and mantle densities of 2.8 and 3.3 x 103 kg m-3, respectively).

5)  If subduction doubled the thickness of the continental crust, calculate the elevation of the resulting plateau.  Assuming that all plateaux are eroded down to sea level, calculate the total thickness of material that would be eroded.